How to differentiate with respect to x, xsin2x.

There are to parts involving x in this expression, so we need to use the product rule. Let u=x and v=sin2x.So we find u'=1, and v'=2sin2x. Then the formula for the product rule gives us that d/dx(uv)= uv' + vu'. so substituting in our values gives us that d/dx(xsin2x) = x(2sin2x) + 1(x) = 2xsin2x + x.